Building Acoustics

Sound transmission 235

will be a discontinuity at the driving point, which is called a bending wave near field.
This field will determine the minimum amount of sound power radiated from a plate, the
plate is of finite or infinite size, when it is driven by single point force or a collection of
such forces. This fact is of great importance in the design of wall linings attached to
heavier walls to minimize radiation (see Chapter 8). Figure 6.19 illustrates a possible
situation at frequencies f < fc, where there is sound radiation caused by edge modes and
bending near field around the excitation point.

Figure 6.19 Sound radiation from a plate excited by a point force. Radiation due to bending wave near field and
edges modes.

The total sound power radiated from a plate having finite dimensions may then be
expressed as

WWac=+ =+near field Wreverberant Wnear field ρ0 0cSu^2 σ. (6.61)

Before treating this expression in more detail and applying it to the problem of impact
sound we shall have a look at the first term, radiation due to the bending near field.

6.4.2.1 Bending wave near field

The radiated power caused by the bending near field may be calculated from an
expression of the bending wave field set up on a thin, infinitely large plate by a point
force. The derivation is given in Cremer et al. (1988) and we shall cite only the end result
which is

22 2

00 0

near field point 22 2 B

0

assuming ,

22

cFk F

WW kk

mcm

ρρ

πω π

== = <<



(6.62)

and where k is the acoustic wave number, the wave number in the surrounding air. We
have presented the first expression to show the analogy with the reverberant part of the
radiated power (see below). However, looking at the second expression we observe that
Wpoint is dependent neither on frequency nor on the bending stiffness. The latter fact may
seem odd, as we know that an increased stiffness will result in a longer wavelength and
thereby an increase in the radiated power. This effect is however offset by an increased
“resistance” against movement; the input impedance is increasing and the mobility will
be less as seen from Equation (6.51). It should be noted that Equation (6.62) applies only
for frequencies below the critical frequency.